In many processes it is necessary to evaporate a liquid in indirect heat exchange with a heat transfer fluid. Heat transfer fluid is understood here to mean any fluid that releases heat, for example a condensing gas. There are two basic forms of such evaporators. Liquid bath evaporators, also called thermosiphon evaporators, stand in a liquid bath, and the evaporation passages are in contact with the liquid bath and the vapor formed exits on top out of the evaporation passages. With falling film evaporators, the liquid flows as a film over the walls of the evaporation passages and thus evaporates partially; the vapor formed flows with the fluid downward and is drained on the lower end of the evaporation passages together with the portion that has remained liquid. Both types have drawbacks. Thus with liquid bath evaporators, the structural height is limited; and with falling film evaporators a pump is needed to circulate liquid because, with the evaporated portion, a certain residual amount of liquid exits that must be circulated. In EP-A469780 it has already been proposed to combine a falling film evaporator and a liquid bath evaporator by connecting them in sequence on the evaporation side. The passages for the heat transfer fluid are arranged in parallel. This device requires a control mechanism that adjusts the distribution of the heat transfer fluid to both of the heat exchangers. For this purpose, at least one pipe must emerge from the housing to a controllable valve. Overall, this proposal results in expensive pipework and a relatively large structural height.